Link-based day-to-day network traffic dynamics and equilibria

A general dynamical system model with link-based variables is formulated to characterize the processes of achieving equilibria from a non-equilibrium state in traffic networks. Several desirable properties of the dynamical system model are established, including the equivalence between its stationary state and user equilibrium, the invariance of its evolutionary trajectories, and the uniqueness and stability of its stationary points. Moreover, it is shown that not only a link-based version of two existing day-to-day traffic dynamics models but also two existing link-based dynamical system models of traffic flow are the special cases of the proposed model. The stabilities of stationary states of these special cases are also analyzed and discussed. In addition, an extension is made to the case with elastic demand. The study is helpful for better understanding the day-to-day adjustment mechanism of traffic flows in networks.     

Dynamic congestion pricing with day-to-day flow evolution and user heterogeneity

This paper investigates evolutionary implementation of congestion pricing schemes to minimize the system cost and time, measured in monetary and time units, respectively, with the travelers’ day-to-day route adjustment behavior and their heterogeneity. The travelers’ heterogeneity is captured by their value-of-times. First, the multi-class flow dynamical system is proposed to model the travelers’ route adjustment behavior in a tolled transportation network with multiple user classes. Then, the stability condition and properties of equilibrium is examined. We further investigate the trajectory control problem via dynamic congestion pricing scheme to derive the system cost, time optimum, and generally, Pareto optimum in the sense of simultaneous minimization of system cost and time. The trajectory control problem is modeled by a differential–algebraic system with the differential sub-system capturing the flow dynamics and the algebraic one capturing the pricing constraint. The explicit Runge–Kutta method is proposed to calculate the dynamic flow trajectories and anonymous link tolls. The method allows the link tolls to be updated with any predetermined periods and forces the system cost and/or time to approach the optimum levels. Both analytical and numerical examples are adopted to examine the efficiency of the method.     

Morning commute problem considering route choice, user heterogeneity and alternative system optima

This paper extends the bottleneck model to study congestion behavior of morning commute and its implications to transportation economics. The proposed model considers simultaneous route and departure time choices of heterogenous users who are distinguished by their valuation of travel time and punctual arrival. Moreover, two dynamic system optima are considered: one minimizes system cost in the unit of monetary value (i.e., the conventional system optimum, or SO) and the other minimizes system cost in the unit of travel time (i.e., the time-based SO, or TSO). Analytical solutions of no-toll equilibrium, SO and TSO are provided and the welfare effects of the corresponding dynamic congestion pricing options are examined, with and without route choice. The analyses suggest that TSO provides a Pareto-improving solution to the social inequity issue associated with SO. Although a TSO toll is generally discriminatory, anonymous TSO tolls do exist under certain circumstances. Unlike in the case with homogenous users, an SO toll generally alters users’ route choices by tolling the poorer users off the more desirable road, which worsens social inequity. Numerical examples are presented to verify analytical results.     

Bayesian network-based formulation and analysis for toll road utilization supported by traffic information provision

Congestion pricing has been proposed and investigated as an effective means of optimizing traffic assignment, alleviating congestion, and enhancing traffic operation efficiencies. Meanwhile, advanced traffic information dissemination systems, such as Advanced Traveler Information System (ATIS), have been developed and deployed to provide real-time, accurate, and complete network-wide traffic information to facilitate travelers’ trip plans and routing selections. Recent advances in ATIS technologies, especially telecommunication technology, allow dynamic, personalized, and multimodal traffic information to be disseminated and impact travelers’ choices of departure times, alternative routes, and travel modes in the context of congestion pricing. However, few studies were conducted to determine the impact of traffic information dissemination on toll road utilizations. In this study, the effects of the provisions of traffic information on toll road usage are investigated and analyzed based on a stated preference survey conducted in Texas. A Bayesian Network (BN)-based approach is developed to discover travelers’ opinions and preferences for toll road utilization supported by network-wide traffic information provisions. The probabilistic interdependencies among various attributes, including routing choice, departure time, traffic information dissemination mode, content, coverage, commuter demographic information, and travel patterns, are identified and their impacts on toll road usage are quantified. The results indicate that the BN model performs reasonably well in travelers’ preference classifications for toll road utilization and knowledge extraction. The BN Most Probable Explanation (MPE) measurement, probability inference and variable influence analysis results illustrate travelers using highway advisory radio and internet as their primary mode of receiving traffic information are more likely to comply with routing recommendations and use toll roads. Traffic information regarding congested roads, road hazard warnings, and accident locations is of great interest to travelers, who tend to acquire such information and use toll roads more frequently. Travel time formation for home-based trips can considerably enhance travelers’ preferences for toll road usage. Female travelers tend to seek traffic information and utilize toll roads more frequently. As expected, the information provided at both pre-trip and en-route stages can positively influence travelers’ preferences for toll road usage. The proposed methodology and research findings advance our previous study and provide insight into travelers’ behavioral tendencies concerning toll road utilization in support of traffic information dissemination.     

Traffic dynamics in a bi-modal transportation network with information provision and adaptive transit services

This paper has two major components. The first one is the day-to-day evolution of travelers’ mode and route choices in a bi-modal transportation system where traffic information (predicted travel cost) is available to travelers. The second one is a public transit operator adjusting or adapting its service over time (from period to period) based on observed system conditions. Particularly, we consider that on each day both travelers’ past travel experiences and the predicted travel cost (based on information provision) can affect travelers’ perceptions of different modes and routes, and thus affect their mode choice and/or route choice accordingly. This evolution process from day to day is formulated by a discrete dynamical model. The properties of such a dynamical model are then analyzed, including the existence, uniqueness and stability of the fixed point. Most importantly, we show that the predicted travel cost based on information provision may help stabilize the dynamical system even if it is not fully accurate. Given the day-to-day traffic evolution, we then model an adaptive transit operator who can adjust frequency and fare for public transit from period to period (each period contains a certain number of days). The adaptive frequency and fare in one period are determined from the realized transit demands and transit profits of the previous periods, which is to achieve a (locally) maximum transit profit. The day-to-day and period-to-period models and their properties are also illustrated by numerical experiments.     

Dynamic user equilibrium with side constraints for a traffic network: Theoretical development and numerical solution algorithm

This paper investigates a traffic volume control scheme for a dynamic traffic network model which aims to ensure that traffic volumes on specified links do not exceed preferred levels. The problem is formulated as a dynamic user equilibrium problem with side constraints (DUE-SC) in which the side constraints represent the restrictions on the traffic volumes. Travelers choose their departure times and routes to minimize their generalized travel costs, which include early/late arrival penalties. An infinite-dimensional variational inequality (VI) is formulated to model the DUE-SC. Based on this VI formulation, we establish an existence result for the DUE-SC by showing that the VI admits at least one solution. To analyze the necessary condition for the DUE-SC, we restate the VI as an equivalent optimal control problem. The Lagrange multipliers associated with the side constraints as derived from the optimality condition of the DUE-SC provide the traffic volume control scheme. The control scheme can be interpreted as additional travel delays (either tolls or access delays) imposed upon drivers for using the controlled links. This additional delay term derived from the Lagrange multiplier is compared with its counterpart in a static user equilibrium assignment model. If the side constraint is chosen as the storage capacity of a link, the additional delay can be viewed as the effort needed to prevent the link from spillback. Under this circumstance, it is found that the flow is incompressible when the link traffic volume is equal to its storage capacity. An algorithm based on Euler’s discretization scheme and nonlinear programming is proposed to solve the DUE-SC. Numerical examples are presented to illustrate the mechanism of the proposed traffic volume control scheme.     

Network operation reliability in a Manhattan-like urban system with adaptive traffic lights

Traffic breakdown to global gridlock occurring in congested traffic network makes the serious traffic congestion even much worse. This paper has proposed to use Network Operation Reliability (NOR) to quantitatively depict the probabilistic feature of traffic breakdown to global gridlock. The Nagel–Schreckenberg cellular automaton model has been used to simulate the traffic flow in a Manhattan-like urban network. A simple adaptive traffic light strategy has been proposed. It has been shown that if vehicles choose to use geometric shortest path, the adaptive traffic signals are able to remarkably enhance the NOR and sometimes the average velocity and the arrival rate as well. The vehicle distribution has been investigated, which has heuristically explained the enhancement of the NOR. A simple perimeter control strategy has been shown to fail to enhance the NOR. Finally, we show that if the time shortest path information could be provided and updated timely, then the NOR can be remarkably enhanced but the adaptive traffic signals have only trivial effect on NOR.     

Spatial and temporal characterization of travel patterns in a traffic network using vehicle trajectories

This paper presents a trajectory clustering method to discover spatial and temporal travel patterns in a traffic network. The study focuses on identifying spatially distinct traffic flow groups using trajectory clustering and investigating temporal traffic patterns of each spatial group. The main contribution of this paper is the development of a systematic framework for clustering and classifying vehicle trajectory data, which does not require a pre-processing step known as map-matching and directly applies to trajectory data without requiring the information on the underlying road network. The framework consists of four steps: similarity measurement, trajectory clustering, generation of cluster representative subsequences, and trajectory classification. First, we propose the use of the Longest Common Subsequence (LCS) between two vehicle trajectories as their similarity measure, assuming that the extent to which vehicles’ routes overlap indicates the level of closeness and relatedness as well as potential interactions between these vehicles. We then extend a density-based clustering algorithm, DBSCAN, to incorporate the LCS-based distance in our trajectory clustering problem. The output of the proposed clustering approach is a few spatially distinct traffic stream clusters, which together provide an informative and succinct representation of major network traffic streams. Next, we introduce the notion of Cluster Representative Subsequence (CRS), which reflects dense road segments shared by trajectories belonging to a given traffic stream cluster, and present the procedure of generating a set of CRSs by merging the pairwise LCSs via hierarchical agglomerative clustering. The CRSs are then used in the trajectory classification step to measure the similarity between a new trajectory and a cluster. The proposed framework is demonstrated using actual vehicle trajectory data collected from New York City, USA. A simple experiment was performed to illustrate the use of the proposed spatial traffic stream clustering in application areas such as network-level traffic flow pattern analysis and travel time reliability analysis.     

Spatial-temporal traffic flow pattern identification and anomaly detection with dictionary-based compression theory in a large-scale urban network

Traffic flow pattern identification, as well as anomaly detection, is an important component for traffic operations and control. To reveal the characteristics of regional traffic flow patterns in large road networks, this paper employs dictionary-based compression theory to identify the features of both spatial and temporal patterns by analyzing the multi-dimensional traffic-related data. An anomaly index is derived to quantify the network traffic in both spatial and temporal perspectives. Both pattern identifications are conducted in three different geographic levels: detector, intersection, and sub-region. From different geographic levels, this study finds several important features of traffic flow patterns, including the geographic distribution of traffic flow patterns, pattern shifts at different times-of-day, pattern fluctuations over different days, etc. Both spatial and temporal traffic flow patterns defined in this study can jointly characterize pattern changes and provide a good performance measure of traffic operations and management. The proposed method is further implemented in a case study for the impact of a newly constructed subway line. The before-and-after study identifies the major changes of surrounding road traffic near the subway stations. It is found that new metro stations attract more commute traffic in weekdays as well as entertaining traffic during weekends.     

Modelling and simulation of transportation system effectiveness to reduce traffic congestion: a system dynamics framework

ABSTRACT

This paper is designed to evaluate and improve the effectiveness of transportation systems and reduce traffic congestion through the use of simulation models and scenario development. A system dynamics framework is used to test and evaluate the alternatives of future strategies for the city of Surabaya, Indonesia. Some factors affecting the effectiveness of transport systems include operational effectiveness and service effectiveness, as well as uncertainty. To improve the effectiveness of transportation systems, several strategies can be implemented, such as subsidizing public transportation, increasing the cost of private vehicle parking fees, raising taxes on private vehicles, and reducing delays in public transportation through scenario development. Scenario results show that, by pursuing these strategies, effectiveness could be improved by 80% as the impact of the increase in operational and service effectiveness, helping to mitigate traffic congestion. Congestion could be reduced to 70% (on average) due to the decrease in daily traffic.     

From user equilibrium to system optimum: a literature review on the role of travel information,bounded rationality and non-selfish behaviour at the network and individual levels

Travel information continues to receive significant attention in the field of travel behaviour research, as it is expected to help reduce congestion by directing the network state from a user equilibrium towards a more efficient system optimum. This literature review contributes to the existing literature in at least two ways. First, it considers both the individual perspective and the network perspective when assessing the potential effects of travel information, in contrast to earlier studies. Secondly, it highlights the role of bounded rationality as well as that of non-selfish behaviour in route choice and in response to information, complementing earlier reviews that mostly focused on bounded rationality only. It is concluded that information strategies should be tailor-made to an individual's level of rationality as well as level of selfishness in order to approach system-optimal conditions on the network level. Moreover, initial ideas and future research directions are provided for assessing the potential of travel information in order to improve network efficiency of existing road networks.     

Evaluating the benefits of a combined route guidance and road pricing system in a traffic network with recurrent congestion

When drivers do not have complete information on road travel time and thus choose their routes in a stochastic manner or based on their previous experience, separate implementations of either route guidance or road pricing cannot drive a stochastic network flow pattern towards a system optimum in a Wardropian sense. It is thus of interest to consider a combined route guidance and road pricing system. A road guidance system could reduce drivers' uncertainty of travel time through provision of traffic information. A driver who is equipped with a guidance system could be assumed to receive complete information, and hence be able to find the minimum travel time routes in a user-optimal manner, while marginal-cost road pricing could drive a user-optimal flow pattern toward a system optimum. Therefore, a joint implementation of route guidance and road pricing in a network with recurrent congestion could drive a stochastic network flow pattern towards a system optimum, and thus achieve a higher reduction in system travel time. In this paper the interaction between route guidance and road pricing is modeled and the potential benefit of their joint implementation is evaluated based on a mixed equilibrium traffic assignment model. The private and system benefits under marginal-cost pricing and varied levels of market penetration of the information systems are investigated with a small and a large example. It is concluded that the two technologies complement each other and that their joint implementation can reduce travel time more efficiently in a network with recurrent congestion.